Philosophy 167: Class 12 - Part 7 - Newton's Mechanics: Laws of Motion for a Theory of Impact, and Some Consequences.
Smith, George E. (George Edwin), 1938-
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Now, the one warning on this, the form in which I've put on assigned reading, the nine page document, is from Paravell's book, which you've already been reading for this week. Paravell's book which doesn't have much annotation. I have put under supplementary material Tom Whiteside's coverage of the same nine handwritten page document which runs about 45 pages cuz it's Latin, English on facing page with more words in the footnotes than in the text.
A good thing about Whiteside is he covers all the math in detail, showing it to you in modern form. The bad thing is it's a whole hell of a lot more reading and I don't feel that good about sticking you with it. So, it's up to you whether you want to read the Whiteside version of or you wanna just read Harrivale with very little annotation.
The physics isn't much different either way and that's what the paper is asking you to write about, the physics. So it's an issue of how much you want to understand the math because Tom is very good on that. I mean that's what he did is exposition. All right any questions about that?
Isaac in the break reminded me of another way I like to describe Newton. This not in anyway reflective of me. Here's a perhaps in some ways the best picture of Newton. Number one, he is one of the two or three greatest experimental physicists in history. You'll see that some in the Principia, but it's the most dramatic in the optics.
It's fairly dramatic in the chemical research, too. Number two, he's almost always listed along with Gauss, those are the two greatest mathematicians in history. Whether he's one of two, or one of five, he's very much up there. And number three, he's always listed, usually with Maxwell, as one of the greatest theoretical physicists in history.
There's nobody else we've every had that's that good at all three. Okay. That's what's unique. So he's constantly having math inform his physics, experiment inform his physics, both of those inform his experiment. Nobody else is in that position. I once had a discussion with Bernard Cohen, who would come closest to him, and then propose what was Fermi.
But Fermi made no serious contributions to mathematics. Huygens was spectacularly good, but his contributions to mathematics were almost negligible side-by-side with Newton's, okay? The evolute method is the primary contribution. So, you know, that's another way to think of it. Of course that doesn't tell you how he got that good at all three.
And I've already told you enough about the experimentation. How patient to do you have to be? To do cross-check experiment after cross-check experiment to see what's going on, you know? All right, I'm going to start in on the material you read for tonight. The first thing is The Laws of Motion paper.
We don't know how to date this. It's clearly in response to Descartes on impact. The problem in dating it is, is it done, it's in English. Newton doesn't start using mostly Latin in a serious writing until after he becomes Lucayan professor. So there's a tendency to want to assign this before 1669 because it's an image.
That's not, you can't really do that reasoning because the whole, the first edition of The Optics, the whole thing it's in English so it's not straightforward It's an interesting question. If it's before 1669, it means he has not seen the three publications in 1669 and field transactions by Wallace Rin and Huygens, with Huygens giving you the full solution for impact of spheres head on, hard, totally elastic spheres head on.
If Newton has not seen that and he's doing this on his own, it's pretty spectacular. If Newton has seen that result, this is less spectacular because it is in some ways derived from it, in other ways it's not derived at all. So we're unsure how to date it.
Per usual, with Newton it's very, very hard to date stuff most of the time. The striking thing about it is Newton's statement of the problem. Everybody else is worried about two spheres impacting head on, but think about Descartes. The only spheres are his globules. The third type of matter is stuff like this, and the first type of matter is irregularly shaped to fill vacuums.
So if you're actually gonna do impact for Descartes, it should be irregular shapes. What does Newton do? Irregular shapes. He poses the problem from the beginning, not as one about spheres in this paper. Now turns out that's not easy to proceed. So motion he defines as bulk times velocity.
Bulk is the word molus same word Huygens was using and others were using. And then this is the next step is very much Descartes. Force is proportional to the change in motion, which is the change in bulk times velocity. So, the amount of force on impact is to be measured by how much change in motion there is.
Okay. Nothing like force occurs in Huygens' work on impact. So Newton is definitely doing that differently and doing it in a term Descartes used. Now, center of motion, the point in a rotating body at which, quote, endeavors, that's Canotis of course, endeavors of it's part every way from the center are exactly counterpoised by opposite endeavors.
The real quantity of circular motion about any axis is proportional to the radius of circulation times the angular velocity times the bulk. Okay? What he wants is angular momentum, of course, that's our current concept and that's what he's pursuing. What's the radius of circulation about any axis? Well, you got to determine that experimentally.
Determine from the experiment in which the entire quantity of circular motion is transferred as translational motion to a body of the same bulk has in the diagram above. So the irregularly shaped object is turning. It will hit the sphere at some point, and at the point at which it stops perfectly its angular motion, and the sphere goes perfectly translationally, it's given all its angular motion to the sphere.
That distance, DC, is the radius of circulation. Okay? He's trying to get what we call the moment of inertia, but he can understand it physically, intuitively, but he has no way to specify it. Nobody specified it before 1750, and it's way older than so it's a long way off.
Huygens comes close but nobody actually succeeds before him. But notice what he's doing here. He can't do the problem analytically so he resorts to an experimental basis in which to do it. Being confident that if he does these experiments he will get a well defined radius of circulation.
Right, that's what's sitting behind this. Now this is Mead, both translational and rotational motion can be resolved in the components and composed from components, in accord with the parallelogram. That's fairly striking, that he does it for both. And, finally, quote everybody keeps the same real quantity of circular motion and velocity, as long as it is not opposed by other bodies.
All right. With that, he reaches conclusions, principles. First one, the points of impact of the two bodies are reflected from one another with the same relative velocity of separation as they had of approach. Now that of course is a fundamental principle in Huygens work but it doesn't show up in the 1669 paper.
Okay Newton could work it out from the solution given there. But it's not featured in the 1669 paper the way it is in the posthumously published paper on collision that we had two or three weeks ago. Second, the changes in the velocities are distributed among the four velocities, two rotational, two translational.
Proportionately to the easiness of their change. And I give it in terms of the diagram up there. That's the Cartesian way of thinking of it, as a contest, but it's not the same contest as Descartes had. It's rather, when the impact occurs, the resulting distribution of the motions, is in some sense minimal.
Minimizing something. Okay? Next. Only those bodies which are absolutely hard, are exactly reflected, in accordance with these principles. So he's making the same concession. Now two key principles in all reflections of any bodies the common center of gravity of the bodies does not change it's state of motion or rest by the reflection of the bodies one amongst another.
Huygens had of course published that in 1669. It's a nice question whether Newton had discovered it beforehand. It's not that hard to understand. If you have bought inertia, it takes something external to change the motion of a body. If it's a system of bodies, then the center of gravity, to change it is gonna require an external force.
Any interactions among them the center of gravity isn't gonna change motion. It's just a generalization of the principle of inertia, okay? And finally, the anti-Descartes motion in the Descartes sense may be lost by reflection. Motion may be gained by reflection. He doesn't say anything about conservation of motion, in the same direction, Huygens does.
At any rate what I give you this paper, partly, I'll get to this in just a moment. Partly to make a couple of points. A, he has very, very good physical intuitions. It's easy to believe that he made toys. For the people at this school cuz he's trading very heavily on a combination of what he knows other people have done plus physical intuition here.
He's quite good at it. Now you're gonna see what we're gonna end up with here is he tries to do experiments, and the experiments don't define things well.